IIT-JEE 2005 Screening | Indefinite Integrals Question 6 | Mathematics

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IIT-JEE 2005 Screening

MCQ (Single Correct Answer)

-0.75

If $$\int\limits_{\sin x}^1 {{t^2}f\left( t \right)dt = 1 - \sin x,} $$ then f$$\left( {{1 \over {\sqrt 3 }}} \right)$$ is

$${1 \over 3}$$

$${{1 \over {\sqrt 3 }}}$$

$$3$$

$${\sqrt 3 }$$

IIT-JEE 1995 Screening

MCQ (Single Correct Answer)

-0.75

The value of the integral $$\int {{{{{\cos }^3}x + {{\cos }^5}x} \over {{{\sin }^2}x + {{\sin }^4}x}}} \,dx\,$$ is

$$\sin x - 6{\tan ^{ - 1}}\left( {\sin x} \right) + c$$

$$\sin x - 2{\left( {\sin x} \right)^{ - 1}} + c$$

$$\sin x - 2{\left( {\sin x} \right)^{ - 1}} - 6{\tan ^{ - 1}}\left( {\sin x} \right) + c$$

$$\,\sin x - 2{\left( {\sin x} \right)^{ - 1}} + 5{\tan ^{ - 1}}\left( {\sin x} \right) + c$$

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